How can we understand intelligent behavior? How can we design intelligent computers? These are questions that have been discussed by scientists and the public at large for over 50 years. As mathematicians, however, the question we want to ask is “is there a mathematical theory underlying intelligence?” I believe the first mathematical attack on these issues was Control Theory, led by Wiener and...

We consider a model of optimal investment and consumption with both habit-formation and partial observations in incomplete Itô processes markets. The individual investor develops addictive consumption habits gradually while he can only observe the market stock prices but not the instantaneous rates of return, which follow Ornstein-Uhlenbeck processes. Applying the Kalman-Bucy filtering theorem ...

We develop computationally fast and storage e cient implementations for the Kalman-Bucy lter (KBf) for data assimilation problems with large time varying multidimensional elds. We refer to them as the block KBf (bKBf) and the localized block KBf (lbKBf). For elds de ned on a 2D lattice of linear dimension I, the bKBf reduces the computational complexity of the KBf by O(I). The lbKBf saves furth...

We propose a novel approximate inference approach for continuous time stochastic dynamical systems observed in both discrete and continuous time with noise. Our expectation-propagation approach generalises the classical Kalman-Bucy smoothing procedure to non-Gaussian observations, enabling continuous-time inference in a variety of models, including spiking neuronal models (state-space models wi...

We study the linear filtering problem for systems driven by continuous Gaussian processes V 1 and V 2 with memory described by two parameters. The processes V j have the virtue that they possess stationary increments and simple semimartingale representations simultaneously. It allows for straightforward parameter estimations. After giving the semimartingale representations of V j by innovation ...

Anti-Ma2 encephalitis is a rare form of autoimmune that has classically been described as paraneoplastic neurobehavioral disorder due to its association with underlying malignancies. We discuss the case 30-year-old female an exceptionally aggressive presentation anti-Ma2 accompanied by Klüver-Bucy syndrome and hypothalamic dysfunction. Her course was complicated repeated aspiration events secon...